Accelerating particle-swarm algorithms

ABSTRACT

Embodiments of the inventive subject matter include determining a plurality of potential full resolution locations for a particle representation for a second iteration of a particle swarm optimization, wherein the particle representation is associated with both a first full resolution location and a first reduced resolution location for a first iteration of the particle swarm optimization that has not yet completed and the second iteration is later than the first iteration. Embodiments further include determining that the plurality of full resolution locations reduces to a second reduced resolution location for the second iteration. Embodiments further include submitting the second reduced resolution location for fitness calculation prior to the first iteration completing.

RELATED MATTER

This application is a Continuation of and claims the priority benefit ofU.S. application Ser. No. 14/529,988 filed Oct. 31, 2014.

BACKGROUND

Embodiments of the inventive subject matter generally relate to thefield of computing, and more particularly, to particle swarmoptimization.

Particle swarm optimization is a metaheuristic optimization thatattempts to find the most optimal solution to a problem. Particle swarmoptimization algorithms search a solution space with “particles.” Duringeach iteration of a particle swarm optimization algorithm, the particlesmove to new locations in the solution space. Each location correspondsto a candidate solution to the problem. Once the location of eachparticle has been determined at a current iteration, the fitness of eachlocation is calculated using a fitness function. After the fitness ofeach location is calculated at the current iteration, a next iterationof the particle swarm optimization algorithm begins and the particlesmove to new locations in the solution space. The process continues untila termination criterion is satisfied.

Typically, a particle's location during the next iteration is dictatedby the most fit location that the particle has occupied (the particle's“personal best”), the most fit location that any of the particles in theswarm has occupied (the “global best”), and the particle's momentum.Because each particle moves about the solution space based on itspersonal best and the global best, each particle tends to move towardthe most fit location. Additionally, because each particle moves aboutthe solution space based on its personal best and the global best, themovement of each particle about the solution space is dependent on thefitness calculations performed during all previous iterations.Consequently, locations of particles at the next iteration cannot bedetermined until the fitness of each particle at the current iterationhas been calculated.

SUMMARY

Embodiments of the inventive subject matter include determining aplurality of potential full resolution locations for a particlerepresentation for a second iteration of a particle swarm optimization,wherein the particle representation is associated with both a first fullresolution location and a first reduced resolution location for a firstiteration of the particle swarm optimization that has not yet completedand the second iteration is later than the first iteration. Embodimentsfurther include determining that the plurality of full resolutionlocations reduces to a second reduced resolution location for the seconditeration. Embodiments further include submitting the second reducedresolution location for fitness calculation prior to the first iterationcompleting.

BRIEF DESCRIPTION OF THE DRAWINGS

The embodiments may be better understood by referencing the accompanyingdrawings.

FIG. 1 depicts a conceptual example of an accelerated particle swarmoptimization.

FIG. 2 is a flow diagram depicting example operations for accelerating aparticle swarm optimization.

FIG. 3 is a flow diagram depicting example operations for updatingpotential personal best lists for each particle in a set and a potentialglobal best list for the set to aid in accelerating a particle swarmoptimization.

FIG. 4 is a flow diagram depicting example operations for using thelists updated in FIG. 3 to calculate potential reduced resolutionlocations for the particles in the set at iteration k+1.

FIG. 5 is a flow diagram depicting example operations for submittingspeculative reduced resolution locations for fitness calculation toaccelerate a particle swarm optimization based on resource utilization.

FIG. 6 depicts an example computer system with a particle swarmoptimization accelerator.

DESCRIPTION OF EMBODIMENT(S)

The description that follows includes example systems, methods,techniques, instruction sequences and computer program products thatembody techniques of the inventive subject matter. However, it isunderstood that the described embodiments may be practiced without thesespecific details. For instance, although examples refer to particlesexisting in two-dimensional space (i.e., each particle has twocoordinates) the scope of the claims are not so limited. Embodiments cansearch an n-dimensional space (i.e., each particle has n coordinates)with n being any integer greater than 0. In other instances, well-knowninstruction instances, protocols, structures and techniques have notbeen shown in detail in order not to obfuscate the description.

Introduction

Typically, particle swarm optimization algorithms utilize two equations,

{right arrow over (v)} _(i) ^(k+1)+ρ_(i) {right arrow over (v)} _(i)^(k) +K _(p) k _(p,i)({right arrow over (x)} _(p,i) ^(x) −{right arrowover (x)} _(i) ^(k))+K _(g) k _(g,i)({right arrow over (x)} _(g) ^(k)−{right arrow over (x)} _(i) ^(k))   1.

{right arrow over (x)} _(i) ^(k+1) ={right arrow over (x)} _(i) ^(k)+{right arrow over (v)} _(i) ^(k+1)   2.

where the superscript k denotes the current iteration; the subscript “i”identifies the particle; the superscript k+1 denotes the next iteration;{right arrow over (v)}_(i) ^(k+1) represents a particle's velocity forthe k+1 iteration; ρ_(i){right arrow over (v)}_(i) ^(k) represents aparticles “momentum” for the k iteration; {right arrow over (x)}_(p,i)^(k) resents the particle's personal best; {right arrow over (x)}_(i)^(k) represents the particle's current location for the k iteration; and{right arrow over (x)}_(g) ^(k) represents the global best as of the kiteration. The expression ({right arrow over (x)}_(p,i) ^(k)−{rightarrow over (x)}_(i) ^(k)) represents a particle's affinity to itspersonal best. The expression ({right arrow over (x)}_(g) ^(k)−{rightarrow over (x)}_(i) ^(k)) represents a particle's affinity to a globalbest. The terms K_(p) and k_(p,i) are constants controlling a particle'saffinity to the particle's personal best, and the terms K_(g), andk_(g,i) are constants controlling a particle's affinity to the globalbest. Particle swarm optimization algorithms typically initialize byplacing the particles at random locations within the solution space. Thefitness of each of the random locations is then calculated. Eachparticle's personal best and a best for all of the particles (i.e., the“global best”) are determined based on these calculations. Once thecalculations are complete, the next iteration of the particle swarmoptimization algorithm can begin. To calculate the fitness of each ofthe locations of the particles during the next iteration, the locationsof the particles at the next iteration are first determined.

Locations of each of the particles at the next iteration are determinedusing the two equations above. The first equation calculates aparticle's velocity ({right arrow over (v)}_(i) ^(k+1)) based on theparticle's momentum (ρ_(i){right arrow over (v)}_(i) ^(k)), theparticle's personal best relative to the particle's current location({right arrow over (x)}_(p,i) ^(k)−{right arrow over (x)}_(i) ^(k)), andthe current global best relative to the particle's current location({right arrow over (x)}_(g,i) ^(k)−{right arrow over (x)}_(i) ^(k)). Thesecond equation determines the particle's location ({right arrow over(x)}_(i) ^(k+1)) based on the particle's velocity ({right arrow over(v)}_(i) ^(k+1)) and the particle's current location ({right arrow over(x)}_(i) ^(k)). Once the location for each particle at the nextiteration is known, the fitness of each of the locations of theparticles is again calculated. The locations for each particle at thenext iteration may result in new personal bests and/or a new globalbest. This process continues until a termination criterion is satisfied.Examples of a termination criterion include completion of a specifiednumber of iterations and a candidate solution falling within a definedrange.

Numerous iterations may be run before a termination criterion issatisfied, but the iterations have sequential dependencies. As describedabove, the location of a particle in iteration k+1 is calculated withthe velocity in iteration k+1 and the location in iteration k. Thevelocity in iteration k+1 is calculated with the global best ofiteration k. Since the global best is not known until the end of aniteration, the particles of iteration k cannot proceed to a location initeration k+1 until the end of iteration k even though the other values(e.g., location in iteration k and momentum) for computing the iterationk+1 velocity are known before the end of iteration k.

Overview

Particle swarm optimization can be accelerated by reducing resolution ofparticles' locations. Reducing resolution of a location can be roundingvalues, eliminating insignificant figures, reducing mathematicalprecision, etc. For example, all particle location values between 1.5and 2.49 will reduce in resolution to a value of 2 (i.e., all valuesbetween 1.5 and 2.49 round to the integer value 2). Reducing resolutionof particles' locations in iteration k reduces the number of potentialparticle locations in iteration k+1. For example, although there may betwo potential full resolution locations for a particle at iteration k+1,the two potential full resolution locations for the particle atiteration k+1 may reduce to the same reduced resolution location. If thetwo potential full resolution locations for the particle at iterationk+1 reduce to the same reduced resolution location, the reducedresolution location for the particle at iteration k+1 is known. Becausethe reduced resolution location for the particle at iteration k+1 isknown, the fitness of the reduced resolution location for the particleat iteration k+1 can be calculated, thus allowing the particle swarmoptimization to be accelerated.

FIG. 1 depicts a conceptual example of an accelerated particle swarmoptimization. The top portion 100 of FIG. 1 depicts a solution space 104at iteration k, a first table 108 including values for particles atiteration k, and two velocity equations 138 and 140 for particles atiteration k. The bottom portion 102 of FIG. 1 depicts the solution space104 at iteration k+1 and a second table 110 including values forparticles at iteration k+1. This discussion will begin with the topportion 100 of FIG. 1.

At iteration k, the solution space 104 includes two particles, A and B.The full resolution location of particle A at iteration k is representedby circle 124 and denoted by the text “A_(k).” As depicted in thesolution space 104, the full resolution location of particle A atiteration k is (1.25, 0.5). The reduced resolution location of particleA at iteration k is represented by circle 122 and denoted by the text“A_(k)′.” As depicted in the solution space 104, the reduced resolutionlocation of particle A at iteration k is (1, 1). Circles 124 and 122(associated with particle A) have solid boundary lines because thefitness of the location of particle A has already been calculated atiteration k. The full resolution location of particle B at iteration kis represented by circle 128 and denoted by the text “B_(k).” Asdepicted in the solution space 104, the full resolution location ofparticle B at iteration k is (4.25, 0.75). The reduced resolutionlocation of particle B at iteration k is represented by circle 126 anddenoted by the text “B_(k)′.” As depicted in the solution space 104, thereduced resolution location of particle B at iteration k is (4, 1).

In the example accelerated particle swarm optimization depicted in FIG.1, the operation for reducing the resolution of particle locations isrounding. The first table 108 includes values associated with particlesA and B at iteration k. The first table 108 includes three columns—afull resolution location column 112, a reduced resolution locationcolumn 114, and a fitness column 116. The first table 108 includes tworows—a first row 118 associated with particle A at iteration k and asecond row 120 associated with particle B at iteration k. The fullresolution location column 112 indicates the X and Y coordinates of thefull resolution locations of particles A and B at iteration k, thereduced resolution column 114 indicates the X and Y coordinates of thereduced resolution locations of particles A and B at iteration k, andthe fitness column 116 includes the calculated fitness for particles Aand B at iteration k. The fitness column 116 includes a calculatedfitness for particle A because the fitness of the location of particle Aat iteration k has been calculated. The fitness of the reducedresolution location of particle A at iteration k is 57. Because thefitness of the location of particle A at iteration k has beencalculated, particle A′s personal best is known at iteration k. Thefitness column 116 does not include a calculated fitness for particle Bat iteration k because the fitness of the location of particle B atiteration k has not yet been calculated. Because the fitness of thelocation of particle B at iteration k has not yet been calculated, thepersonal best for particle B at iteration k is not known. Rather, thereexist two potential personal bests for particle B at iteration k. Thefirst potential personal best for particle B at iteration k is thepersonal best for particle B at iteration k−1 (the previous iteration).The second potential personal best for particle B at iteration k is thelocation of particle B at iteration k. Put simply, until the fitness ofthe location of particle B at iteration k is calculated, it is not knownwhether the location of particle B at iteration k is more fit than thepersonal best for particle B at iteration k−1.

The equation {right arrow over (v)}^(k+1)=ρ_(i){right arrow over(v)}^(k)+K_(p)k_(p,i)({right arrow over (x)}_(p,i) ^(k)−{right arrowover (x)}_(i) ^(k))+K_(g)k_(g,i)({right arrow over (x)}_(g) ^(k)−{rightarrow over (x)}_(i) ^(k)) is used to determine the velocity of eachparticle. The velocity of each particle is used, in concert with eachparticle's current location, to determine the location of each particleat the next iteration. As previously discussed, the velocity equationincludes three terms. The first term (ρ_(i){right arrow over (v)}^(k))is based on a particle's momentum; the second term ({right arrow over(x)}_(p,i) ^(k)−{right arrow over (x)}_(i) ^(k)) is based on theparticle's affinity to the particle's personal best; and the third term({right arrow over (x)}_(g) ^(k)−{right arrow over (x)}_(i) ^(k)) isbased on the particle's affinity to the global best. The two equations138 and 140 are broken down based on these three terms, where iV₁ (iindicates the particle) represents the first term based on theparticle's momentum; iV₂ represents the second term based on theparticle's personal best; and iV₃ represents the third term based on theglobal best. The first term (iV₁) is not dependent on fitnesscalculations performed. The second and third terms (iV₂ and iV₃,respectively) are dependent on fitness calculations performed.Specifically, the second term (iV₂) is dependent on fitness calculationsperformed for the particle (i.e., the particle's personal best) and thesecond term (iV₃) is dependent on fitness calculations performed for theswarm (i.e., the global best).

The first equation 138 is associated with particle A. At iteration k forparticle A, the first term (AV₁) and the second term (AV₂) are known,but the third term (AV₃) is not known. The second term (AV₂) is knownbecause the fitness of the location of particle A at iteration k hasbeen calculated (i.e., the personal best for particle A at iteration kis known). The solution space 104 includes vectors represented as solidlines that are associated with known terms AV₁ and AV₂. The third term(AV₃) is not known because the fitness of the location of particle B atiteration k is not known (i.e., the global best for the swarm atiteration k is not known). Although the global best at iteration k isnot known, there exist only two potential global bests at iteration k.The first potential global best is the global best for the swarm atiteration k−1 (assuming that the fitness of the global best for theswarm at iteration k−1 is greater than 57). The second potential globalbest for the swarm is the location of particle B at iteration k. Becausethere are two potential global bests, the solution space includes twovectors represented by hashed lines that are associated with the unknownterm AV₃. Each of the two AV₃ hashed lines is associated with one of thepotential global bests. For example, if the global best at iteration kis the global best for the swarm at iteration k−1, the upper AV₃ hashedline indicates the full resolution location of particle A at iterationk+1. If the global best at iteration k is the location of particle B atiteration k, the lower AV₃ hashed line indicates the full resolutionlocation of particle A at iteration k+1. However, whether the upper AV₃hashed line or the lower AV₃ hashed line indicates the full resolutionlocation of particle A at iteration k+1, the reduced resolution locationof particle A at iteration k+1 will be the same. Put simply, theinfluence of the term AV₃ is such that no matter which of the twopotential global bests is determined to be the global best for iterationk, the reduced resolution location of particle A at iteration k+1 willbe the same. The second table 110 includes the two potential fullresolution locations for particle A at iteration k+1 that are associatedwith the upper and lower AV₃ hashed lines. The two potential fullresolution locations for particle A at iteration k+1 are (4.75, 2.25)and (5.25, 1.75), as shown by rows 156 and 158 of the second table 110.Based on the rounding operation used in this example, both of thepotential full resolution locations of particle A at iteration k+1reduce to the same reduced resolution location (5, 2). This is shown insolution space 104 as both the upper and lower AV₃ hashed lines indicatefull resolution locations that fall within box 130. In this example, box130 has vertices (4.5, 1.5), (5.49, 1.5), (5.49, 2.49), and (4.5, 2.49).Based on the rounding operation used in this example, any point thatfalls within box 130 will have a reduced resolution location of (5, 2).Consequently, regardless of which of the two potential global bests isthe global best for iteration k, the reduced resolution location ofparticle A at iteration k+1 is (5, 2). Because there is only one reducedresolution location for particle A at iteration k+1, the reducedresolution location for particle A at iteration k+1 is known. Thereduced resolution location of particle A at iteration k+1 isrepresented by circle 146 in the solution space 104 in the lower portion102 of FIG. 1 and is denoted by the text “A_(k+1)′.” Because the reducedresolution location of particle A at iteration k+1 is known, the fitnessof the reduced resolution of particle A at iteration k+1 can becalculated. As shown in column 154 of the first table 110, the fitnessof the reduced resolution location for particle A at iteration k+1 is71.

The second equation 140 is associated with particle B. At iteration kfor particle B, the first term (BV₁) is known but the second term (BV₂)and third term (BV₃) are not known. The second term (BV₂) is not knownbecause the personal best for particle B at iteration k is not known.The third term (BV₃) is not known because the global best for the swarmat iteration k is not known. As with the lines associated with thevectors for particle A, the lines associated with the vectors forparticle B are solid if the term represented by the vector is known andhashed if the term represented by the vector is unknown. Consequently,the line associated with the BV₁ vector is solid and the linesassociated with both the BV₂ and BV₃ vectors are hashed. Based on thevectors associated with particle B at iteration k, there are fourpotential full resolution locations for particle B at iteration k+1 andthree potential reduced resolution locations for particle B at iterationk+1. The first two potential full resolution locations for particle B atiteration k+1 are (0.75, 2.25) and (1.75, 1.75), as indicated in rows160 and 162 of the second table 110, and fall within boxes 132 and 134,respectively. All full resolution locations within box 132 have areduced resolution location of (1, 2), and all full resolution locationswithin box 134 have a reduced resolution location of (2, 2).Consequently, the first two reduced resolution locations for particle Bat iteration k+1 are (1, 2) and (2, 2). The second two potential fullresolution locations for particle B at iteration k+1 are (6.5, 0.75) and(7.25, 0.75), as indicated by rows 164 and 166 of the second table 110,and fall within box 136. All full resolution locations within box 136have a reduced resolution location of (7, 1). Consequently, there arethree potential reduced resolution locations for particle B at iterationk+1. The three potential reduced resolution locations for particle B atiteration k+1 are (1, 2), (2, 2), and (7, 1), as indicated by rows 160,162, 164, and 166 of the second table 110. The first potential reducedresolution location for particle B at iteration k+1 (i.e., the first“B_(k+1)′?”) is represented by circle 142 in the solution space 104 ofthe lower portion 102 of FIG. 1 and denoted by the text “B_(k+1)′.” Thesecond potential reduced resolution location for particle B at iterationk+1 (i.e., the second “B_(k+1)′?”) is represented by circle 144 in thesolution space 104 of the lower portion 102 of FIG. 1 and denoted by thetext “B_(k+1)′.” The third potential reduced resolution location forparticle B at iteration k+1 (i.e., the third and fourth“B_(k+1)′?”) isrepresented by circle 148 in the solution space 104 of the lower portion102 of FIG. 1 and denoted by the text “B_(k+1)′.” The fitness of each ofthe potential reduced resolution locations of particle B at iterationk+1 has not been calculated, as indicated by the “null” values in column154 of the second table 110. The fitness of each of the potentialreduced resolution locations for particle B have not been calculatedbecause the actual reduced resolution location of particle B atiteration k+1 is not known (i.e., there are three potential reducedresolution locations for particle B at iteration k+1). It should benoted that although the fitness of each of the potential reducedresolution locations for particle B at iteration k+1 have not beencalculated, in some embodiments, the fitness of potential reducedresolution locations can be calculated (see discussion of FIG. 5).

Although the fitness of the locations of all of the particles in theswarm (i.e., particle A and particle B) at iteration k have not beencalculated, embodiments of the inventive subject matter allowdetermination of locations of at least some of the particles at the nextiteration (iteration k+1). As can be seen in FIG. 1, the reducedresolution location of particle A at iteration k+1 can be determinedeven though the global best for the swarm at iteration k is not yetknown. Because of this resolution reduction, the example particle swarmoptimization is accelerated and fitness calculations can begin foriteration k+1 before iteration k completes.

FIG. 2 is a flow diagram depicting example operations for accelerating aparticle swarm optimization. The flow begins at block 202. Theacceleration of particle swarm into iteration k+1 occurs while iterationk of the particle swarm optimization is still running. For instance,while a first thread performs operations for particle swarm optimizationin an iteration k, a second thread can be triggered to accelerate intoiteration k+1. The second thread begins operations for the particles'reduced resolution locations at the current iteration (i.e., iterationk) and determines whether a single reduced resolution location can bedetermined for any of the particles at the next iteration (i.e.,iteration k+1).

At block 202, a particle in a particle swarm optimization is selectedfor iteration k+1 evaluation. When the second thread is invoked (i.e.,when the acceleration begins) a particle is selected from the particleswarm. The flow continues at block 204.

At block 204, the potential full resolution location(s) for the selectedparticle at iteration k+1 are determined. As previously mentioned,locations of particles at iteration k+1 are determined based on threevectors—a first vector based on the particle's momentum, a second vectorbased on the particle's personal best, and a third vector based on theglobal best. If the fitness of the locations of each of the particles atiteration k has been calculated, all three vectors are known and thefull resolution location of the selected particle (as well as thereduced resolution location of the selected particle) at iteration k+1is known. If the fitness of the location of the selected particle atiteration k has been calculated but the fitness of the locations ofother particles at iteration k have not been calculated, only the firsttwo vectors are known (e.g., see particle A in FIG. 1) and there mayexist multiple potential full resolution locations for the selectedparticle at iteration k+1. If the fitness of the location of theselected particle at iteration k has not been calculated, only the firstvector is known (e.g., see particle B in FIG. 1) and there may existmultiple potential full resolution locations for the selected particleat iteration k+1. The flow continues at block 206.

At block 206, the potential reduced resolution location(s) for theselected particle at iteration k+1 are determined based on thedetermined full resolution locations. The reduced resolution location(s)for the selected particle are based on resolution reduction of the fullresolution location(s) of the selected particle determined at block 204.As previously discussed, the resolution of particle locations can bereduced by rounding values, eliminating insignificant figures, reducingmathematical precision, etc. In some embodiments, the resolutionreduction is dependent on the granularity of real world materials. Forexample, a particle swarm optimization can be used to determine theoptimal resistance of a resistor, inductance of an inductor, and lengthof a connecting wire in a computer chip. While a solution space mayinclude values with a higher degree of resolution (e.g., precision tothe one hundred thousandths place or greater), the granularity of thematerials may require a range of finite values. For example, thepossible resistances for a resistor may be in 1 Ω increments; thepossible inductances of an inductor may be in 0.5 mH increments; and thepossible connecting wire lengths may be in 0.25 mm increments. In suchan embodiment, the resolution of a particle's location can be reduced tomatch these increments (e.g., a resistance value of 3.61 Ω would reduceto 4 Ω, an inductance of 3.3 mH would reduce to 3.5 mH, and a wirelength of 1.11 mm would reduce to 1.0 mm). The flow continues at block208.

At block 208, the number of potential reduced resolution locations forthe selected particle at iteration k+1 is determined. As discussedabove, the number of potential full resolution locations for eachparticle at iteration k+1 depends on whether the fitness of the reducedresolution locations of all particles in the swarm at iteration k havebeen calculated. However, even though there may exist more than onepotential full resolution location for the selected particle atiteration k+1, the multiple potential full resolution locations for theselected particle at iteration k+1 may reduce in resolution to only onepotential reduced resolution location for the selected particle atiteration k+1 (e.g., see particle A in FIG. 1). In such a case, thereduced resolution location of the selected particle at iteration k+1 isknown. The flow continues at decision diamond 210.

At decision diamond 210, if the number of potential reduced resolutionlocation(s) of the selected particle at iteration k+1 is greater thanone (i.e., the reduced resolution location of the selected particle atiteration k+1 is not known), the flow continues at block 216 where thenext particle in the particle swarm optimization is selected. If thereis only one potential reduced resolution location for the selectedparticle at iteration k+1 (i.e., the reduced resolution location of theselected particle at iteration k+1 is known), the flow continues atblock 212.

At block 212, the reduced resolution location of the selected particleat iteration k+1 is submitted for fitness calculation. For example, thereduced resolution location of the selected particle at iteration k+1 isadded to a fitness calculation queue. Because the reduced resolutionlocation of the selected particle at iteration k+1 is known, calculatingthe fitness of the reduced resolution location of the selected particleat iteration k+1 efficiently uses resources (i.e., because the reducedresolution location of the selected particle at iteration k+1 is known,no superfluous calculation are performed). The flow continues atdecision diamond 214.

At decision diamond 214, if there are particles remaining (i.e., if theexample operations for accelerating a particle swarm optimization havenot been completed for each particle in the particle swarmoptimization), the flow continues at block 216 where the next particleis selected. If there are no particles remaining (i.e., if the exampleoperations for accelerating a particle swarm optimization have beencompleted for each particle in the particle swarm optimization), theflow ends.

FIG. 3 is a flow diagram depicting example operations for updatingpotential personal best lists for each particle in a set and a potentialglobal best list for the particles in the set to aid in accelerating aparticle swarm optimization. A particle set can be all of the particlesin a swarm, or can be a sub-swarm, containing fewer than all of theparticles in the swarm. In some embodiments, as depicted by theoperations of FIG. 3, a second thread begins operations for theparticles in the set to create and update a potential personal best listfor each particle while a first thread performs operations for particleswarm optimization in an iteration k. Each potential personal best listincludes all potential personal bests for a corresponding particle atiteration k, based on the progress that the first thread has made in theparticle swarm optimization. Additionally the second thread performsoperations for the particles in the set to create and update a potentialglobal best list for the set. The potential global best list includesall potential global bests for the set at iteration k, based on theprogress that the first thread has made in the particle swarmoptimization. In some embodiments, the second thread will not beginperforming the operations of FIG. 3 until a specified number (e.g.,percentage) of particles have been evaluated by the first thread. Forexample, the second thread may not begin the operations of FIG. 3 untilthe first thread has evaluated 50% of the particles at iteration k.After the operations of FIG. 3 have been completed for all particles inthe set, the flow continues to FIG. 4. FIG. 4 is a flow diagramdepicting example operations for using the lists updated in FIG. 3 tocalculate potential reduced resolution locations for the particles ofthe set at iteration k+1, and if appropriate, submitting the potentialreduced resolution locations for the particles of the set at iterationk+1 for fitness evaluation. The operations of FIG. 3 begin at block 302.

At block 302, an i value is initialized to equal one. The i value isinitialized to one so that the first particle in the set is selected. Asthe second thread performs the operations of FIG. 3 for the particles,the i value is incremented so that the operations of FIG. 3 should beperformed for all particles in the set. The flow continues at block 304.

At block 304, particle i is selected from the set. For example, when thei value is initialized to one, the first particle in the set isselected. After the operations of FIG. 3 have been completed once, the ivalue is incremented to two and the second particle in the set isselected, and so on and so forth. The flow continues at decision diamond306.

At decision diamond 306, it is determined whether the fitness of thereduced resolution location of particle i at iteration k has beencalculated. If the fitness of the reduced resolution location ofparticle i at iteration k has been calculated, the flow continues atdecision diamond 314. If the fitness of the reduced resolution locationof particle i at iteration k has not been calculated, the flow continuesat block 308.

At block 308, the reduced resolution location of particle i at iterationk is added to a potential personal best list for particle i. Because thefitness of the reduced resolution location of particle i at iteration khas not been calculated, it is unknown whether the fitness of thereduced resolution location of particle i at iteration k is greater thanthe fitness of the personal best for particle i at the previousiteration (i.e., iteration k−1). Because it is not known whether thefitness of the reduced resolution location of particle i at iteration kis greater than the fitness of the personal best for particle i atiteration k−1, there exist two potential personal bests for particle iat iteration k−1 (i.e., the reduced resolution location of particle i atiteration k and the personal best for particle i at iteration k−1).Consequently, the potential personal best list for particle i atiteration k includes two entries, the reduced resolution location ofparticle i at iteration k and the personal best for particle i atiteration k−1. The flow continues at block 310.

At block 310, the reduced resolution location of particle i at iterationk is added to the potential global best list for the swarm. Because thefitness of the reduced resolution location of particle i at iteration khas not been calculated, it is unknown whether the fitness of thereduced resolution location of particle i at iteration k is greater thanthe fitness of any other reduced resolution locations in the potentialglobal best list. Consequently, after completion of the operations ofFIG. 3, the potential global best list will include the reducedresolution location of each particle in the set for which the fitnesshas not been calculated and the reduced resolution location of thecurrent global best (i.e., either the reduced resolution location of theglobal best at iteration k−1 or the reduced resolution location of oneof the particles of the swarm at iteration k for which the fitness hasbeen calculated). The flow continues at decision diamond 312.

At decision diamond 312, the i value is compared to set_size (i.e., thenumber of particles in the set). If the i value is equal to set_size,then the operations of FIG. 3 have been performed on all particles inthe set. In other words, the potential personal best list for eachparticle in the set has been updated at iteration k and the potentialglobal best list for the set includes all potential global bests for theset at iteration k. If the i value equals set_size, the flow continuesat block 402 of FIG. 4. If the i value is not equal to set_size, theflow continues at block 322.

At block 322, the i value is incremented. The i value is incremented sothat the next particle in the set can be selected and the operations ofFIG. 3 repeat at block 304 where particle i is selected.

As previously discussed at decision diamond 306, if the fitness of thereduced resolution location of particle i at iteration k has beencalculated, the flow continues at decision diamond 314. At decisiondiamond 314, it is determined whether the fitness of the reducedresolution location of particle i at iteration k is greater than thefitness of the current personal best for particle i (i.e., the personalbest for particle i at iteration k−1). The personal best for particle iat iteration k−1 is the reduced resolution location that particle i hasoccupied in any iteration prior to iteration k with the greatestfitness.

There are two possible outcomes from the determination made at decisiondiamond 314. The first possible outcome is that the fitness of thereduced resolution location of particle i at iteration k is not greaterthan the fitness of the personal best for particle i at iteration k−1.If the fitness of the reduced resolution location of particle i atiteration k is not greater than the fitness of the personal best forparticle i at iteration k−1, the flow continues at decision diamond 312to determine whether all particles in the set have been considered. Ifthe fitness of the reduced resolution location of particle i atiteration k is not greater than the fitness of the personal best forparticle i at iteration k−1, the reduced resolution location of particlei at iteration k cannot be a global best for the set. Because thereduced resolution location of particle i at iteration k cannot be aglobal best for the set, it is not necessary to perform the operationsof decision diamond 318 and block 320. If the fitness of the reducedresolution location of particle i at iteration k is not greater than thefitness of the personal best for particle i at iteration k−1, thepersonal best for particle i at iteration k−1 is the personal best forparticle i at iteration k. Put simply, the personal best for particle iat iteration k−1 remains the personal best for particle i at iterationk. Consequently, the potential personal best list for particle i willinclude only one potential personal best (i.e., the personal best forparticle i at iteration k−1).

The second possible outcome is that the fitness of the reducedresolution location of particle i at iteration k is greater than thefitness of the personal best for particle i at iteration k−1. If thefitness of the reduced resolution location of particle i at iteration kis greater than the fitness of the personal best for particle i atiteration k−1, the flow continues at block 316.

At block 316, the potential personal best list for particle i is updatedto replace the personal best for particle i at iteration k−1 with thereduced resolution location of particle i at iteration k. Because thefitness of the reduced resolution location of particle i at iteration kis greater than the fitness of the personal best for particle i atiteration k−1, the reduced resolution location of particle i atiteration k is the most fit location that particle i has occupied and isthe personal best for particle i at iteration k. After the operations atblock 316 have been completed for particle i, the potential personalbest list for particle i will include only one potential personal best(i.e., the reduced resolution location of particle i at iteration k)because the personal best for particle i at iteration k is the reducedresolution location of particle i at iteration k. In some embodiments, afitness value associated with the reduced resolution location ofparticle i at iteration k is also indicated in the potential personalbest list. The flow continues at decision diamond 318.

At decision diamond 318, it is determined whether the fitness of thereduced resolution location particle i at iteration k is greater thanthe fitness of the current global best for the set (i.e., the globalbest for the set at iteration k−1). If the fitness of the reducedresolution location of particle i at iteration k is not greater than thefitness of the global best for the set at iteration k−1, the flowcontinues at decision diamond 312 where the i value is compared toset_size. If the fitness of the reduced resolution location of particlei at iteration k is greater than the fitness of the global best for theset at iteration k−1, the flow continues at block 320.

At block 320, the potential global best list is updated to replace theglobal best for the set at iteration k−1 with the reduced resolutionlocation of particle i at iteration k. Because the fitness of thereduced resolution location of particle i at iteration k is greater thanthe fitness of the global best for the set at iteration k−1, the reducedresolution location of particle i at iteration k is the most fitlocation that any particle in the set has occupied and is now thecurrent global best for the set. As previously discussed at block 310,the potential global best list will include the new current global best(i.e., the reduced resolution location of particle i at iteration k) andthe reduced resolution locations of all particles at iteration k forwhich the fitness is still unknown. In some embodiments, the fitnessvalue associated with the reduced resolution location of particle i atiteration k is also indicated in the potential global best list. Theflow continues at decision diamond 312.

At decision diamond 312, if the i value is not equal to set_size, theflow continues at block 322 where the i value is incremented. If the ivalue is equal to set_size, the operations of FIG. 3 have been completedfor all particles in the set and the flow continues at block 402 of FIG.4.

FIG. 4 is a flow diagram depicting example operations for using thelists updated in FIG. 3 to calculate potential reduced resolutionlocations for the particles of the set at iteration k+1. The operationsof FIG. 4 perform operations for all particles in the set and, using thelist updated in FIG. 3, calculate potential reduced resolution locationsfor the particles in the set at iteration k+1. If there exists only onepotential reduced resolution location for a particle at iteration k+1,the reduced resolution location of the particle at iteration k+1 issubmitted for fitness calculation. If there exist more than onepotential reduced resolution location for the particle at iteration k+1,the more than one potential reduced resolution locations for theparticle at iteration k+1 are not submitted for fitness calculation andthe operations of FIG. 4 are performed on the next particle in the set.In some embodiments, the operations of FIG. 4 may not begin unless thereare fewer than a threshold number of potential global bests. Forexample, FIG. 4 can include a conditional that checks the number ofpotential global bests in the potential global best list beforeselecting a particle from the set for iteration k+1 locationcalculation. If the number of potential global bests in the potentialglobal best list exceeds a threshold, the operations of FIG. 4 can besuspended until the first thread has evaluated enough particles atiteration k for the potential global best list to include fewer than thethreshold number of potential global bests. The operations of FIG. 4begin at block 402.

At block 402, the i value is reinitialized to a value of one. The ivalue is reinitialized to a value of one because the operations of FIG.4 are repeated for each particle in the set. The operations of FIG. 4perform operations for the particles in the set to determine a number ofpotential reduced resolution locations that exist for each particle inthe set at iteration k+1. The flow continues at block 404.

At block 404, particle i is selected from the set for iteration k+1location calculation. The flow continues at block 406.

At block 406, a value (“x_(k+1)”) representing potential reducedresolution locations for particle i at iteration k+1 is initialized to anull value. The x_(k+1) value is initialized to null because nopotential reduced resolution locations for particle i at iteration k+1have been computed. When a reduced resolution location for particle i atiteration k+1 is computed, the x_(k+1) value is updated based on thereduced resolution location of particle i at iteration k+1 that wascomputed (i.e., x_(k+1) is set to the reduced resolution location ofparticle i at iteration k+1). The flow continues at block 408.

At block 408, operations begin in which each potential global best inthe potential global best list is used to compute reduced resolutionlocations for particle i at iteration k+1. The flow continues at block410.

At block 410, operations begin in which each potential personal best inthe potential personal best list for particle i is used to computereduced resolution locations for particle i at iteration k+1. Block 410in conjunction with block 408 uses all potential personal bests forparticle i and all potential global bests for the set to compute allpossible reduced resolution location for particle i at iteration k+1.For example, if the potential global best list includes three potentialglobal bests (i.e., G₁, G₂, and G₃) and the potential personal best listfor particle i includes two potential personal bests for particle i(i.e., P₁ and P₂), there are six combinations of global bests andpersonal bests that can be used to compute potential reduced resolutionlocations for particle i at iteration k+1. The six possible combinationsare 1) G₁ and P₁, 2) G₁ and P₂, 3) G₂ and P₁, 4) G₂ and P₂, 5) G₃ andP₁, and 6) G₃ and P₂. In other words, for the first potential globalbest (i.e., G₁), potential reduced resolution locations for particle iat iteration k+1 are computed using each of the first potential personalbest (i.e., P₁) and the second potential personal best (i.e., P₂). Forthe second potential global best (i.e., G₂), potential reducedresolution locations for particle i at iteration k+1 are computed usingeach of the first potential personal best (i.e., P₁) and the secondpotential personal best (i.e., P₂). For the third potential global best(i.e., G₃), potential reduced resolution locations for particle i atiteration k+1 are computed using the first potential personal best(i.e., P₁) and the second potential personal best (i.e., P₂). The flowcontinues at block 412.

At block 412, potential reduced resolution locations for particle i atiteration k+1 (“y_(k+1)”) are computed. In the example discussed above,during each permutation of the operations initiated at block 408 and410, a different one of the six combinations of potential global bestsand personal bests are used to compute a potential reduced resolutionlocation for particle i at iteration k+1. The flow continues at decisiondiamond 414.

At decision diamond 414, it is determined whether the x_(k+1) value isnull. If the x_(k+1) value is null, it is the first permutation of theoperations initiated at blocks 408 and 410 and the y_(k+1) valuecomputed at block 412 is the first y_(k+1) value computed for particlei. If the x_(k+1) value is null, the flow continues at block 416. Atblock 416, the reduced resolution location for particle i at iterationk+1 is set to the computed location at block 412 (i.e., the x_(k−1)value is set to the y_(k+1) value) and the flow continues at block 420.At block 420, another permutation of the operations initiated at block410 begins (assuming there exist potential personal bests that have notbeen used to calculate a potential reduced resolution location forparticle i at iteration k+1). If the x_(k−1) value is not null, thecurrent permutation of the operations initiated at blocks 408 and 410 isnot the first permutation of the operations and the flow continues atdecision diamond 418.

At decision diamond 418, the x_(k+)1 value is compared to the locationcomputed at block 412 (i.e., x_(k+1)=y_(k+1)?). If the x_(k+1) value andthe y_(k+1) value are the same, the location computed at block 412 inthe current permutation of the operations initiated at blocks 408 and410 is the same as the location computed at block 412 in all previouspermutations of the operations initiated at blocks 408 and 410. If thex_(k+1) value is not the same as the y_(k+1) value, the locationcalculated at block 412 in the current permutation of the operationsinitiated at blocks 408 and 410 is not the same as the location computedat block 412 for the previous permutation(s) of the operations initiatedat blocks 408 and 410. If the x_(k+1) value is not the same as they_(k+1) value, there exists more than one potential reduced resolutionlocation for particle i at iteration k+1. If the x_(k+1) value is notthe same as the y_(k+1) value, the flow continues at decision diamond426 (i.e., the operations initiated at blocks 408 and 410 areterminated). The operations initiated at blocks 408 and 410 areterminated because there exists more than one potential reducedresolution location for particle i at iteration k+1 (i.e., the reducedresolution of particle i at iteration k+1 is not known). If the x_(k+1)value is the same as the y_(k+1) value, the location computed at block412 in the current permutation of the operations initiated at blocks 408and 410 is the same as all locations computed at block 412 in previouspermutations of the operations initiated at blocks 408 and 410. Becausethe x_(k+1) value is the same as the y_(k+1) value, there is currentlyonly one potential reduced resolution location for particle i atiteration k+1. If the x_(k+1) value is the same as the y_(k+1) value,the flow continues at block 420.

At block 420, if there are remaining potential personal bests in thepotential personal best list for particle i (i.e., there are potentialpersonal bests remaining in the personal best list for particle i thathave not been used to compute a potential reduced resolution locationfor particle i at iteration k+1 for the current permutation of theoperations initiated at block 408), the flow continues at block 410. Atblock 410, another permutation of the operations initiated at block 410begins. If there are no remaining potential personal bests in thepersonal best list for particle i (i.e., all potential personal bests inthe potential personal best list for particle i have been used tocalculate a potential reduced resolution location for particle i atiteration k+1 for the current permutation of the operations initiated atblock 408), the flow continues at block 422.

At block 422, if there are remaining potential global bests in thepotential global best list that have not been used to calculatepotential reduced resolution locations for particle i at iteration k+1,the flow continues at block 408. At block 408, another permutation ofthe operations initiated at block 408 begins. If all potential globalbests in the potential global best list have been used to calculatereduced resolution locations of particle i at iteration k+1 (i.e., thereare no remaining global bests in the potential global best list), theflow continues at block 424.

At block 424, the reduced resolution location of particle i at iterationk+1 (y_(k+1)) is submitted for fitness calculation. If the operationsinitiated at blocks 408 and 410 have successfully completed potentialreduced resolution location calculation for all potential personal bestsfor particle i and all potential global bests without terminating, thereexists only one potential reduced resolution location for particle i atiteration k+1. Because there exists only one potential reducedresolution location for particle i at iteration k+1, the reducedresolution location of particle i at iteration k+1 is known. Because thereduced resolution location of particle i at iteration k+1 is known, thereduced resolution location of particle i at iteration k+1 is submittedfor fitness calculation. The flow continues at decision diamond 426.

At decision diamond 426, the i value is compared to set_size. If the ivalue equals set_size, iteration k+1 location calculations have beenperformed for all particles in the set. If iteration k+1 locationcalculations have been performed for all particles in the set, the flowends. If the i value does not equal set_size, iteration k+1 locationcalculations have not been performed for all particles in the set andthe flow continues at block 428.

At block 428, the i value is incremented. The i value is incremented sothat the next particle in the set can be selected for iteration k+1location calculations. The flow continues until iteration k+1 locationcalculations have been completed for all particles in the set.

The operations depicted in FIGS. 3 and 4 are provided as examples anddifferent embodiments of the inventive subject matter may employ moreoperations than depicted in FIGS. 3 and 4, fewer operations thandepicted in FIGS. 3 and 4, or operations different from those depictedin FIGS. 3 and 4. For example, although the discussion of FIGS. 3 and 4describe creating and updating lists to indicate potential personalbests for a particle and potential global bests for a set of particles,embodiments are not so limited. Any suitable data structure may be usedindicate potential personal bests for a particle and potential globalbests for a set of particles. For example, hash tables, arrays, or setscan be used instead of lists to indicate potential personal bests for aparticle and potential global bests for a set of particles.Additionally, although FIG. 4 checks a y_(k+1) value against an x_(k−1)value at decision diamond 418 to determine whether more than onepotential reduced resolution location for a particle at iteration k+1exists, this is but one example and many suitable alternatives exist.For example, during each permutation of the operations initiated atblocks 408 and 410, a data structure (e.g., a set, a list, etc.)associated with the particle can be updated to include the y_(k+1) valuecomputed at block 412. After the data structure is updated, a check canbe performed to determine whether the data structure includes more thanone unique potential reduced resolution location. Alternatively, thischeck can be performed after all permutations of the operationsinitiated at block 408 and 410 have completed for the particle. Finally,some embodiments of the inventive subject matter may utilize a morespeculative approach than that described in the discussion of FIG. 4(e.g., see discussion of FIG. 5). For example, although the operationsof FIG. 4 will not submit a reduced resolution location of a particlefor fitness calculation unless the reduced resolution location of theparticle at iteration k+1 is known, some embodiments allow multiplepotential reduced resolution locations for a particle at iteration k+1to be submitted for fitness calculation. In some embodiments, athreshold value can be defined. If a particle has fewer potentialreduced resolution locations at iteration k+1 than the threshold, thepotential reduced resolution locations are submitted for fitnesscalculation. For example, if the threshold value is four and a particlehas three potential reduced resolution locations at iteration k+1, allthree potential reduced resolution locations for the particle atiteration k+1 will be submitted for fitness calculation. Although onlyone of the three potential reduced resolution locations will be thereduced resolution location of the particle at iteration k+1, this morespeculative analysis could yield new personal and/or global bests. Insome embodiments, this more speculative analysis can be reserved fortimes when there exist available computing resources. In suchembodiments, this more speculative analysis can potentially provide newpersonal and/or global bests while efficiently using computingresources.

FIG. 5 is a flow diagram depicting example operations for submittingspeculative locations for fitness calculation to accelerate a particleswarm optimization based on resource utilization. If resources areavailable, speculative locations can be submitted for fitnesscalculation. For example, if there are an insufficient number of reducedresolution locations awaiting fitness calculation to efficiently utilizeavailable resources, then speculative locations can be submitted forfitness calculation to use the underutilize resources for the fitnesscalculation queue. Some embodiments of the inventive subject matterutilize two or more fitness calculation queues. For example, a firstfitness calculation queue includes reduced resolution locations forparticles at iteration k and a second fitness calculation queue includesreduced resolution locations for particles at iteration k+1. In suchembodiments, different processing resources are used to perform fitnesscalculations for the reduced resolution locations in each fitnesscalculation queue. For example, a first processor can perform fitnesscalculations for reduced resolution locations in the first fitnesscalculation queue and a second processor can perform fitnesscalculations for reduced resolution locations in the second fitnesscalculation queue. In such embodiments, speculative locations are addedto the second fitness calculation queue. Utilization of separate fitnesscalculation queues can ensure that acceleration operations in iterationk+1 do not interfere with the operations in iteration k.

The operations of FIG. 5 provide example operations for submittingspeculative locations for fitness calculation. In some embodiments, theoperations of FIG. 5 begin after the operations of FIGS. 3 and 4 arecomplete for a given iteration. After the operations of FIGS. 3 and 4,all known particle locations (i.e., reduced resolution locations) atiteration k+1 have been submitted for fitness calculation. Although allknown particle locations at iteration k+1 have been submitted forfitness calculation, there may still be available processing resources.To ensure efficient use of resources, speculative locations can besubmitted for fitness calculation. In some embodiments, the speculativelocations have the same degree of precision as the reduced resolutionlocations. The flow begins at decision diamond 502.

At decision diamond 502, it is determined whether there are availableprocessing resources. For example, the number of reduced resolutionlocations awaiting fitness calculation (i.e., the number of reducedresolution locations in a fitness queue) can be used as a proxy forresource utilization. In such embodiments, if the number of reducedresolution locations awaiting fitness calculation is below a threshold,it is assumed that there exist available resources. This threshold canbe a static value. For example, the threshold can be set so that whenthere are fewer than five reduced resolution locations awaiting fitnesscalculation, speculative locations will be submitted for fitnesscalculation. Alternatively, this threshold can vary dependent uponprogress of the particle swarm optimization. For example, if the fitnessof fewer than 33% of the reduced resolution locations of particles in aset at iteration k has been calculated, the threshold is 10. If thefitness of fewer than 66% but greater than 33% of the reduced resolutionlocations of particles in the set at iteration k has been calculated,the threshold is five. And if the fitness of more than 66% of thereduced resolution locations of particles in the set at iteration k hasbeen calculated, the threshold is two. If there are no availableresources, the flow ends. If there are available resources, the flowcontinues at block 504.

At block 504, speculative locations are determined. Speculativelocations can be determined using a variety of determination techniques.Each of blocks 508, 510, and 512 describe an example determinationtechnique. In some embodiments, the determination technique that is usedis dependent on a level of resource utilization. For example, if thelevel of available processing resource is low, minimally speculativedetermination techniques can be used (e.g., the determination techniqueof block 508). If the level of available processing resource is high,more speculative determination techniques can be used (e.g., randomlocations within a solution space can be chosen as speculativelocations). Each of the example determination techniques described inblocks 508, 510, and 512 will be discussed below. Although three exampledetermination techniques are provided in FIG. 5, other determinationtechniques may be used and the determination techniques of FIG. 5 arenot limited to these three example determination techniques. Forexample, random locations can be chosen as speculative locations orlocations near any of the particles' personal bests can be chosen asspeculative locations. After the speculative locations are determined,the flow continues at block 506.

A first example determination technique is described at block 508. Atblock 508, speculative locations are determined from a group ofpotential reduced resolution locations for a particle at iteration k+1.For example, if a particle has two potential reduced resolutionlocations at iteration k+1, one or both of the potential reducedresolution locations for the particle at iteration k+1 can be chosen asspeculative locations. Although it is not known which of the twopotential reduced resolution locations for the particle at iteration k+1will be the reduced resolution location of the particle at iterationk+1, it can be worthwhile to calculate the fitness of one or both of thepotential reduced resolution locations for the particle at iteration k+1if processing resources are currently available.

A second example determination technique is described at block 510. Atblock 510, speculative locations can be determined based on a currentglobal best. For example, speculative locations can be chosen fromlocations adjacent to or near the current global best. As stated, thenumber of speculative locations adjacent to the global best chosen forfitness calculation can vary with the level of available resources, butcan also vary with other factors or may not vary from a predefinednumber. As an example of other factors that influence selection, thenumber of locations adjacent to a global best can vary based on thenumber of iterations passed and/or quality of the current global best.The speculative locations adjacent to the current global best can bechosen randomly or chosen based on personal bests of n most fitparticles. Adjacency of locations can be defined as any locations of thereduced resolution within a given distance of the global best. Thisgiven distance can vary based on proximity of other particles, variancein previous global bests, etc.

A third example determination technique is described at block 512. Atblock 512, speculative locations can be determined based on a currentglobal best and a current personal best for one of the particles of theset. For example, speculative locations can be chosen from locationsresiding on a line between the current global best and the currentpersonal best for the one of the particles.

As previously discussed, after the speculative locations are determinedat block 504, the flow continues at block 506. At block 506, thespeculative locations are submitted for fitness calculation. Forexample, the speculative locations can be added to a fitness calculationqueue. As previously discussed, in some embodiments, there exists morethan one fitness calculation queue. In such embodiments, the speculativelocations can be added to a fitness calculation queue including reducedresolution locations for particles at iteration k+1. Alternatively,speculative locations can be added to their own fitness calculationqueue. For example, some embodiments include a fitness calculation queuethat includes only speculative locations.

Although FIG. 5 describes using a number of reduced resolution locationsawaiting fitness calculation as a metric for resource utilization,another metric for resource utilization can be used. For example,processor usage can be monitored. If processor usage falls below aspecified level, the operations of FIG. 5 are initiated and speculativereduced resolution locations are submitted for fitness calculation.Additionally, although the discussion of FIG. 5 describes the operationsof FIG. 5 working in concert with the operations of FIGS. 3 and 4, insome embodiments, the operations of FIG. 5 work independently, orirrespective, of the operations of FIGS. 3 and 4. For example, insteadof waiting for the operations of FIGS. 3 and 4 to complete, theoperations of FIG. 5 can be triggered at random or predeterminedintervals. In such embodiments, resource utilization is checkedperiodically. If during a periodic check it is determined that there areavailable resources, speculative reduced resolution locations aredetermined and submitted for fitness calculation. As another example,resource utilization can be monitored continuously. In such embodiments,whenever there are available resources, speculative reduced resolutionlocations are determined and submitted for fitness calculation.

As will be appreciated by one skilled in the art, aspects of theinventive subject matter may be embodied as a system, method or computerprogram product. Accordingly, aspects of the inventive subject mattermay take the form of an entirely hardware embodiment, an entirelysoftware embodiment (including firmware, resident software, micro-code,etc.) or an embodiment combining software and hardware aspects that mayall generally be referred to herein as a “circuit,” “module” or“system.” Furthermore, aspects of the inventive subject matter may takethe form of a computer program product embodied in one or more computerreadable medium(s) having computer readable program code embodiedthereon.

Any combination of one or more computer readable medium(s) may beutilized. The computer readable medium may be a computer readable signalmedium or a computer readable storage medium. A computer readablestorage medium may be, for example, but not limited to, an electronic,magnetic, optical, electromagnetic, infrared, or semiconductor system,apparatus, or device, or any suitable combination of the foregoing. Morespecific examples (a non-exhaustive list) of the computer readablestorage medium would include the following: an electrical connectionhaving one or more wires, a portable computer diskette, a hard disk, arandom access memory (RAM), a read-only memory (ROM), an erasableprogrammable read-only memory (EPROM or Flash memory), an optical fiber,a portable compact disc read-only memory (CD-ROM), an optical storagedevice, a magnetic storage device, or any suitable combination of theforegoing. In the context of this document, a computer readable storagemedium may be any tangible medium that can contain, or store a programfor use by or in connection with an instruction execution system,apparatus, or device.

A computer readable signal medium may include a propagated data signalwith computer readable program code embodied therein, for example, inbaseband or as part of a carrier wave. Such a propagated signal may takeany of a variety of forms, including, but not limited to,electro-magnetic, optical, or any suitable combination thereof. Acomputer readable signal medium may be any computer readable medium thatis not a computer readable storage medium and that can communicate,propagate, or transport a program for use by or in connection with aninstruction execution system, apparatus, or device.

Program code embodied on a computer readable medium may be transmittedusing any appropriate medium, including but not limited to wireless,wireline, optical fiber cable, RF, etc., or any suitable combination ofthe foregoing.

Computer program code for carrying out operations for aspects of theinventive subject matter may be written in any combination of one ormore programming languages, including an object oriented programminglanguage such as Java, Smalltalk, C++ or the like and conventionalprocedural programming languages, such as the “C” programming languageor similar programming languages. The program code may execute entirelyon the user's computer, partly on the user's computer, as a stand-alonesoftware package, partly on the user's computer and partly on a remotecomputer or entirely on the remote computer or server. In the latterscenario, the remote computer may be connected to the user's computerthrough any type of network, including a local area network (LAN) or awide area network (WAN), or the connection may be made to an externalcomputer (for example, through the Internet using an Internet ServiceProvider).

Aspects of the inventive subject matter are described with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems) and computer program products according to embodiments of theinventive subject matter. It will be understood that each block of theflowchart illustrations and/or block diagrams, and combinations ofblocks in the flowchart illustrations and/or block diagrams, can beimplemented by computer program instructions. These computer programinstructions may be provided to a processor of a general purposecomputer, special purpose computer, or other programmable dataprocessing apparatus to produce a machine, such that the instructions,which execute via the processor of the computer or other programmabledata processing apparatus, create means for implementing thefunctions/acts specified in the flowchart and/or block diagram block orblocks.

These computer program instructions may also be stored in a computerreadable medium that can direct a computer, other programmable dataprocessing apparatus, or other devices to function in a particularmanner, such that the instructions stored in the computer readablemedium produce an article of manufacture including instructions whichimplement the function/act specified in the flowchart and/or blockdiagram block or blocks.

The computer program instructions may also be loaded onto a computer,other programmable data processing apparatus, or other devices to causea series of operational steps to be performed on the computer, otherprogrammable apparatus or other devices to produce a computerimplemented process such that the instructions which execute on thecomputer or other programmable apparatus provide processes forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks.

FIG. 6 depicts an example computer system with a particle swarmoptimization accelerator. A computer system includes a processor unit602 (possibly including multiple processors, multiple cores, multiplenodes, and/or implementing multi-threading, etc.). The computer systemincludes memory 606. The memory 606 may be system memory (e.g., one ormore of cache, SRAM, DRAM, zero capacitor RAM, Twin Transistor RAM,eDRAM, EDO RAM, DDR RAM, EEPROM, NRAM, RRAM, SONOS, PRAM, etc.) or anyone or more of the above already described possible realizations ofmachine-readable media. The computer system also includes a bus 604(e.g., PCI, ISA, PCI-Express, HyperTransport® bus, InfiniBand® bus,NuBus bus, etc.), a network interface 618 (e.g., an ATM interface, anEthernet interface, a Frame Relay interface, SONET interface, wirelessinterface, etc.), and a storage device(s) 620 (e.g., optical storage,magnetic storage, etc.). The computer system also includes a particleswarm optimization accelerator (“accelerator”) 608. This accelerator 608uses reduced resolution of locations to accelerate the particle swarmoptimization into a next iteration as described above. Any one of thefunctionalities may be partially (or entirely) implemented in hardwareand/or on the processing unit 602. For example, the functionality may beimplemented with an application specific integrated circuit, in logicimplemented in the processing unit 602, in a co-processor on aperipheral device or card, etc. Further, realizations may include feweror additional components not illustrated in FIG. 6 (e.g., video cards,audio cards, additional network interfaces, peripheral devices, etc.).The processor unit 602, the storage device(s) 620, and the networkinterface 618 are coupled to the bus 604. Although illustrated as beingcoupled to the bus 604, the memory 606 may be coupled to the processorunit 602.

While the embodiments are described with reference to variousimplementations and exploitations, it will be understood that theseembodiments are illustrative and that the scope of the inventive subjectmatter is not limited to them. In general, techniques for accelerating aparticle swarm optimization as described herein may be implemented withfacilities consistent with any hardware system or hardware systems. Manyvariations, modifications, additions, and improvements are possible.

Plural instances may be provided for components, operations orstructures described herein as a single instance. Finally, boundariesbetween various components, operations and data stores are somewhatarbitrary, and particular operations are illustrated in the context ofspecific illustrative configurations. Other allocations of functionalityare envisioned and may fall within the scope of the inventive subjectmatter. In general, structures and functionality presented as separatecomponents in the example configurations may be implemented as acombined structure or component. Similarly, structures and functionalitypresented as a single component may be implemented as separatecomponents. These and other variations, modifications, additions, andimprovements may fall within the scope of the inventive subject matter.

Use of the phrase “at least one of . . . or” should not be construed tobe exclusive. For instance, the phrase “X comprises at least one of A,B, or C” does not mean that X comprises only one of {A, B, C}; it doesnot mean that X comprises only one instance of each of {A, B, C}, evenif any one of {A, B, C} is a category or sub-category; and it does notmean that an additional element cannot be added to the non-exclusive set(i.e., X can comprise {A, B, Z}).

What is claimed is:
 1. A method for accelerating a particle swarmoptimization, the method comprising: determining a plurality ofpotential full resolution locations for a particle representation for asecond iteration of a particle swarm optimization, wherein the particlerepresentation is associated with both a first full resolution locationand a first reduced resolution location for a first iteration of theparticle swarm optimization that has not yet completed and the seconditeration is later than the first iteration; determining that theplurality of full resolution locations reduces to a second reducedresolution location for the second iteration; and submitting the secondreduced resolution location for fitness calculation prior to the firstiteration completing.
 2. The method of claim 1, wherein determining theplurality of potential full resolution locations comprises determiningthe plurality of potential full resolution locations based, at least inpart, on a set of one or more personal bests for the particlerepresentation for the first iteration and a plurality of potentialglobal bests for the first iteration.
 3. The method of claim 2, whereinthe plurality of potential global bests is based, at least in part, on aglobal best for a third iteration that precedes the first iteration andreduced resolution locations for the first iteration for a plurality ofparticle representations for which fitness has yet to be determined. 4.The method of claim 1, further comprising: determining a secondplurality of potential full resolution locations for the seconditeration for a second particle representation; determining that thesecond plurality of potential full resolution locations does not reduceto a single reduced resolution location for the second particlerepresentation for the second iteration; and waiting for fitness to becomputed for at least one additional particle representation for thefirst iteration before attempting to accelerate again.
 5. The method ofclaim 1 further comprising: determining that fitness of the firstreduced resolution location has been computed prior to determining theplurality of potential full resolution locations.
 6. The method of claim1, wherein determining that the plurality of full resolution locationsreduces to the second reduced resolution location comprises at least oneof rounding, truncating, eliminating insignificant figures, and reducingmathematical precision of the plurality of potential full resolutionlocations.
 7. The method of claim 1 further comprising determining areduction in full resolution to reduced resolution based, at least inpart, on resolution of parameters for a problem, wherein the locationsrepresent candidate solutions to the problem.
 8. The method of claim 1further comprising: determining that processing resources are available;determining speculative reduced resolution locations; and submitting thespeculative reduced resolution locations for fitness calculation.
 9. Themethod of claim 8, wherein determining that processing resources areavailable comprises determining that a number of reduced resolutionlocations submitted for fitness calculation for the second iteration isbelow a threshold.
 10. An apparatus comprising: a processor; and acomputer readable storage medium having computer usable program codeembodied therewith, the computer usable program code executable by theprocessor to cause the apparatus to: determine a plurality of potentialfull resolution locations for a particle representation for a seconditeration of a particle swarm optimization, wherein the particlerepresentation is associated with both a first full resolution locationand a first reduced resolution location for a first iteration of theparticle swarm optimization that has not yet completed and the seconditeration is later than the first iteration; determine that theplurality of full resolution locations reduces to a second reducedresolution location for the second iteration; and submit the secondreduced resolution location for fitness calculation prior to the firstiteration completing.
 11. The apparatus of claim 10, wherein the programcode executable by the processor to cause the apparatus to determine theplurality of potential full resolution locations comprises program codeexecutable by the processor to cause the apparatus to determine theplurality of potential full resolution locations based, at least inpart, on a set of one or more personal bests for the particlerepresentation for the first iteration and a plurality of potentialglobal bests for the first iteration.
 12. The apparatus of claim 11,wherein the plurality of potential global bests is based, at least inpart, on a global best for a third iteration that precedes the firstiteration and reduced resolution locations for the first iteration for aplurality of particle representations for which fitness has yet to bedetermined.
 13. The apparatus of claim 10, wherein the program codeexecutable by the processor to cause the apparatus to determine that theplurality of full resolution locations reduces to the second reducedresolution location comprises at least one of rounding, truncating,eliminating insignificant figures, and reducing mathematical precisionof the plurality of potential full resolution locations.
 14. Theapparatus of claim 10, wherein the computer usable program code furtherincludes computer usable program code to: determine a reduction in fullresolution to reduce resolution based, at least in part, on resolutionof parameters for a problem, wherein the locations represent candidatesolutions to the problem.
 15. The apparatus of claim 10, wherein thecomputer usable program code further includes computer usable programcode to: determine that processing resources are available; determinespeculative reduced resolution locations; and submit the speculativereduced resolution locations for fitness calculation.
 16. A computerprogram product for accelerating a particle swarm optimization, thecomputer program product comprising: a computer readable storage mediumhaving computer usable program code embodied therewith, the computerusable program code comprising a computer usable program code to:determine a plurality of potential full resolution locations for aparticle representation for a second iteration of a particle swarmoptimization, wherein the particle representation is associated withboth a first full resolution location and a first reduced resolutionlocation for a first iteration of the particle swarm optimization thathas not yet completed and the second iteration is later than the firstiteration; determine that the plurality of full resolution locationsreduces to a second reduced resolution location for the seconditeration; and submit the second reduced resolution location for fitnesscalculation prior to the first iteration completing.
 17. The computerprogram product of claim 16, wherein the computer usable program code todetermine a plurality of potential full resolution locations comprisescomputer usable program code to determine the plurality of potentialfull resolution locations based, at least in part, on a set of one ormore personal bests for the particle representation for the firstiteration and a plurality of potential global bests for the firstiteration.
 18. The computer program product of claim 17, wherein theplurality of potential global bests is based, at least in part, on aglobal best for a third iteration that precedes the first iteration andreduced resolution locations for the first iteration for a plurality ofparticle representation for which fitness has yet to be determined. 19.The computer program product of claim 16, wherein the computer usableprogram code to determine that the plurality of full resolutionlocations reduces to the second reduced resolution location comprises atleast one of rounding, truncating, eliminating insignificant figures,and reducing mathematical precision of the plurality of potential fullresolution locations.
 20. The computer program product of claim 16,wherein the computer readable storage medium further has stored thereincomputer usable program code to: determine a reduction in fullresolution to reduce resolution based, at least in part, on resolutionof parameters for a problem, wherein the locations represent candidatesolutions to the problem.